A259333 Triangle read by rows: T(n,k) = number of column-convex polyominoes with bond-perimeter 2*n+2 and k columns (1 <= k <= n).

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 37, 16, 1, 1, 25, 105, 106, 25, 1, 1, 36, 240, 446, 245, 36, 1

Offset

1,5

Links

Table of n, a(n) for n=1..28.

M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. [Scanned copy, with permission. A very large file.] See Figure 9.

M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. (Annotated scanned copy of a small part of the thesis)

M.-P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.

S. Dulucq, Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)

Formula

There is an explicit formula for T(n,k) - see Delest (1987), Theorem 24.

Example

Triangle begins:
1,
1,1,
1,4,1,
1,9,9,1,
1,16,37,16,1,
1,25,105,106,25,1,
1,36,240,446,245,36,1,
...

Crossrefs

Row sums are A006027.

Sequence in context: A174006 A124216 A008459 * A180960 A157192 A154982

Adjacent sequences: A259330 A259331 A259332 * A259334 A259335 A259336

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Jun 24 2015

Status

approved